Axis option specification summary of Python "numpy.sum (...)"
Introduction
A summary of the ** axis options ** that can be specified with numpy.ndarray.sum (...) or numpy.ndarray.mean (...). I will explain using figures for 2D and 3D numpy arrays.
For a two-dimensional numpy array
First, target a two-dimensional (ndim = 2) numpy array. As an example, consider the following ** 3 rows 4 columns ** ** 2D numpy array ** </ font> x.
This array x can be generated with the following code.
shape=(3,4)Generate a numpy array of
import numpy as np
x = np.arange(1,12+1).reshape(3,4)
print(x)
#print(x.ndim) # -> 2
#print(x.shape) # -> (3, 4)
Execution result
[ [ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12] ]
Specify ʻaxis = None`
Since ʻaxis = Noneis the default argument, bothx.sum ()andx.sum (axis = None)` have the same behavior. Reference for numpy.sum (...) / numpy.ndarray.sum (...)
sum(axis=None)
s = x.sum(axis=None)
# print(type(s)) # -> <class 'numpy.int64'>
# print(s.ndim) # -> 0
# print(s.shape) # -> ()
print(s)
If ʻaxis = None` is specified, the sum of ** all the elements that make up the array ** will be calculated. Specifically, $ 1 + 2 + 3 + \ cdots + 11 + 12 = $ $ \ bf {78} $ </ font> is calculated.
Execution result
78
Specify ʻaxis = 0`
sum(axis=0)
s = x.sum(axis=0)
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 1
# print(s.shape) # -> (4,)
print(s)
Execution result
[15 18 21 24]
If you specify ʻaxis = 0, the elements are ** summed in the row direction **. Specifically, $ 1 + 5 + 9 = $ <font color ='red'> $ \ bf {15} $ </ font>, $ 2 + 6 + 10 = $ <font color ='red'> $ \ bf {18} $ </ font>, $ 3 + 7 + 11 = $ <font color ='red'> $ \ bf {21} $ </ font>, $ 4 + 8 + 12 = $ <font color ='red' > $ \ Bf {24} $ </ font> is calculated to be [15 18 21 24]`.
** [Caution]: The elements are summed in the row direction (the direction in which the row becomes 0, 1, 2, 3, ...), not the sum of the elements in each row. Please note that ** </ font> (If you misunderstand here, you will fall into ??? at once (experience story)).
Specify ʻaxis = 1`
sum(axis=1)
s = x.sum(axis=1)
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 1
# print(s.shape) # -> (3,)
print(s)
Execution result
[10 26 42]
If ʻaxis = 1is specified, the elements are summed in the ** column direction (the direction in which the column becomes larger as 0, 1, 2, 3, ...) **. Specifically, $ 1 + 2 + 3 + 4 = $ <font color ='red'> $ \ bf {10} $ </ font>, $ 5 + 6 + 7 + 8 = $ <font color ='red' > $ \ bf {26} $ </ font>, $ 9 + 10 + 11 + 12 = $ <font color ='red'> $ \ bf {42} $ </ font> is calculated[10 26 42 ] `.
For 3D numpy arrays
Next, we will target a 3D numpy array. As an example, we'll work with the numpy array x with shape (3,4,2).
shape=(3,4,2)Generate a numpy array of
import numpy as np
x = np.arange(1,24+1).reshape(3,4,2)
print(x)
# print(x.ndim) # -> 3
# print(x.shape) # -> (3, 4, 2)
Execution result (line break position etc. are formatted for readability)
[ [ [ 1 2] [ 3 4] [ 5 6] [ 7 8] ]
[ [ 9 10] [11 12] [13 14] [15 16] ]
[ [17 18] [19 20] [21 22] [23 24] ] ]
If you draw separately with ʻaxis = 2`, it will be as follows.
Specify ʻaxis = None`
sum(axis=None)
s = x.sum(axis=None)
# print(type(s)) # -> <class 'numpy.int64'>
# print(s.ndim) # -> 0
# print(s.shape) # -> ()
print(s)
** Total for all elements **. Specifically, $ 1 + 2 + 3 + 4 + \ cdots + 22 + 23 + 24 = 300 $ is calculated.
Execution result
300
Specify ʻaxis = 0`
sum(axis=0)
s = x.sum(axis=0)
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 2
# print(s.shape) # -> (4, 2)
print(s)
Execution result
[ [27 30]
[33 36]
[39 42]
[45 48] ]
By specifying ʻaxis = 0`, the elements are summed in the ** row direction **.
The first element [27 30] of the above execution result is $ 1 + 9 + 17 = $ $ \ bf {27} $ </ font>, $ 2 + 10 + 18 = $ It is the result calculated as $ \ bf {30} $ </ font>.
x, which was shape = (3,4,2), becomes shape = (4,2) withx.sum (axis = 0).
Specify ʻaxis = 1`
sum(axis=1)
s = x.sum(axis=1)
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 2
# print(s.shape) # -> (3, 2)
print(s)
Execution result
[ [16 20]
[48 52]
[80 84] ]
By specifying ʻaxis = 1, the elements are summed in the ** column direction **. The first element [16 20]` of the above execution result is $ 1 + 3 + 5 + 7 = $ $ \ bf {16} $ </ font>, $ 2 + 4 + 6 + It is the result calculated as 8 = $ $ \ bf {20} $ </ font>.
x, which was shape = (3,4,2), becomes shape = (3,2) withx.sum (axis = 1).
Specify ʻaxis = 2`
sum(axis=2)
s = x.sum(axis=2)
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 2
# print(s.shape) # -> (3, 4)
print(s)
Execution result
[ [ 3 7 11 15]
[19 23 27 31]
[35 39 43 47] ]
By specifying ʻaxis = 2, the elements are summed in the ** channel direction ** if it is an image. The first upper left element 3 of the above execution result is $ 1 + 2 = $ <font color ='red'> $ \ bf {3} $ </ font>, and the lower right element 47` is $ 23 + 24 = It is the result calculated as $ $ \ bf {47} $ </ font>.
x, which was shape = (3,4,2), becomes shape = (3,4) withx.sum (axis = 2).
Specify ʻaxis = (0,1) `
Starting with NumPy 1.7, you can specify the axis as a tuple.
By specifying ʻaxis = (0,1), ** totals for rows and columns ** are calculated. The result is the same even if ʻaxis = (1,0) (the order does not matter).
sum(axis=(0,1))
s = x.sum(axis=(0,1))
#print(type(s)) # -> <class 'numpy.ndarray'>
#print(s.ndim) # -> 1
#print(s.shape) # -> (2,)
print(s)
Execution result
[144 156]
The first element 144 of the execution result is the result of calculating the sum of all the elements ofx [:,:, 0], that is, $ 1 + 3 + 5 + 7 + \ cdots + 19 + 21 + 23 $. Become.
x, which was shape = (3,4,2), becomes shape = (2,) withx.sum (axis = (0,1)).
Specify ʻaxis = (1,2) `
The same is true for ʻaxis = (2,1)`.
sum(axis=(1,2))
s = x.sum(axis=(1,2))
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 1
# print(s.shape) # -> (3,)
print(s)
Execution result
[ 36 100 164]
The first element 36 of the execution result is the sum of the elements in the blue frame in the figure below **, that is, $ (1 + 3 + 5 + 7) + (2 + 4 + 6 + 8) $ is calculated. The result is.
x, which was shape = (3,4,2), becomes shape = (3,) withx.sum (axis = (1,2)).
Specify ʻaxis = (0,2) `
The same is true for ʻaxis = (2,0)`.
sum(axis=(0,2))
s = x.sum(axis=(0,2))
# print(type(s)) # -> <class 'numpy.ndarray'>
# print(s.ndim) # -> 1
# print(s.shape) # -> (4,)
print(s)
Execution result
[57 69 81 93]
The first element 57 of the execution result is the result of calculating the ** total of the elements in the blue frame ** in the figure below, that is, $ (1 + 9 + 17) + (2 + 10 + 18) $. ..
x, which was shape = (3,4,2), becomes shape = (4,) withx.sum (axis = (0,2)).
Specify ʻaxis = (0,1,2) `
sum (axis = (0,1,2)) is the same assum (axis = None)orsum ()and the sum of all elements is calculated.
sum(axis=(0,1,2))
s = x.sum(axis=(0,1,2))
#print(type(s)) # -> <class 'numpy.int64'>
#print(s.ndim) # -> 0
#print(s.shape) # -> ()
print(s)
Execution result
300
x, which was shape = (3,4,2), becomes shape = (0) withx.sum (axis = (0,1,2)).
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